A fixed-point algorithm for second-order total variation models in image denoising

Abstract

In this paper, we construct fixed-point algorithms for the second-order total variation models through discretization models and the subdifferential and proximity operators. Particularly, we focus on the convergence conditions of our algorithms by analyzing the eigenvalues of the difference matrix. The algorithms are tested on various images to verify our proposed convergence conditions. The experiments compared with the split Bregman algorithms demonstrate that fixed-point algorithms could solve the second-order functional minimization problem stably and effectively. Keywords Fixed-point algorithm • Convergence • High-order total variation • Image denoising Mathematics Subject Classification 68U10 • 65K10 Supported by NSF of China (11431015), NSF of Guangdong (2016A030313048), ministry of education in Guangdong for excellent young teachers.

RETRACTED: A compensating total variation image denoising model combining L1 and L2 norm

“…Therefore, a large number of improved algorithms have appeared in the image denoising methods based on the TV model. [17][18][19][20][21][22][23][24][25][26][27] In order to remove noise as much as possible and protect the edges and textures, this paper designed a new compensating TV model combining L 1 and L 2 norm, which can select the diffusion mode for different regions adaptively. Based on the TV model, this new model constructs a regular term that compensates for the TV model.…”